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1 Unit 1: Pure Mathematics A

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Question 157

In triangle OABOABOAB, OA⃗=a\vec{OA} = \mathbf{a}OA=a and OB⃗=b\vec{OB} = \mathbf{b}OB=b.

The point P P\,P divides AB AB\,AB in the ratio AP:PB=2:1AP : PB = 2 : 1AP:PB=2:1, and Q Q\,Q is the midpoint of OAOAOA. The line segments OP OP\,OP and BQ BQ\,BQ intersect at RRR.

a.

Find OP⃗\vec{OP}OP and OQ⃗\vec{OQ}OQ​ in terms of a\mathbf{a}a and b\mathbf{b}b.

[3]
b.

Show that R R\,R is the midpoint of BQ BQ\,BQ and find the ratio OR:RPOR : RPOR:RP.

[4]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
  2. /Maths
  3. /1 Unit 1: Pure Mathematics A

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